Quant Question Of The Day: 161
Geometry
Increasing the radius of a cylinder by 6 units increased the volume by y cubic units. Increasing the height of the cylinder by 6 units also increases the volume by y cubic units. If the original height is 2, then the original radius is:
1. 2
2. 4
3. 6
4. 6π
5. 8
We know that the value of a cylinder is πr2h, where r and h are the radius and height respectively. So, we know that 2π(r +6)2 – 2πr2 = y = πr2 (2 + 6) – 2πr2. Expanding and rearranging, we get that 2π(12r +36) = 6πr². Divide both sides by 6π to get that 4r + 12 = r2, and rearrange to see that r2 – 4r – 12 = 0. This factors to become (r-6) (r + 2) = 0. So, r = 6 or r = -2. Obviously, the radius cannot be negative, so our answer is 6.
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